Abstract

In this paper, using the maximal embedding of SU(2) into SU(N) in the Euler angles parametrization, we construct a novel family of exact solutions of the Einstein SU(N)-Skyrme model. First, we present a hairy toroidal black hole in D=4 dimensions. This solution is asymptotically locally anti-de Sitter and is characterized by discrete hair parameters. Then, we perform a dimensional extension of the black hole to obtain black p-branes as solutions of the Einstein SU(N)-nonlinear sigma model in D?5 dimensions. These are homogeneous and topologically protected. Finally we show that, through a Wick rotation of the toroidal black hole, one can construct an exact self-gravitating instanton. The role that the flavor number N plays in the geometry and thermodynamics of these configurations is also discussed. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.